Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 1: Exercise - 1

For a cubical block, error in measurement of sides is $+ 1\%$ and error in measurement of mass is $+ 2\%$, then maximum possible error in density is,

To estimate $g$ (from $g=4{\pi }^2\frac{L}{T^2}$ ), error in measurement of $L$ is $+ 2\%$ and error in measurement of $T$ is $+ 3\%$. The error in estimated $g$ will be, 

The dimensions of a rectangular block measured with a vernier calipers having least count of $0.1 \mathrm{mm}$ is $5 \mathrm{mm} \times 10 \mathrm{mm} \times 5 \mathrm{mm}$. The maximum percentage error in measurement of volume of the block is

An experiment measures quantities $x\mathit{,}\mathit{ }y\mathit{,}\mathit{ }z$ and then $t$ is calculated from the data as $t=\frac{x{y}^2}{z^3}$. If percentage errors in $x\mathit{,}\mathit{ }y$ and $z$ are respectively $1\%, 3\%, 2\%$, then percentage error in $t$ is:

The external and internal diameters of a hollow cylinder are measured to be $(4.23 \pm 0.01) \mathrm{cm}$ and $(3.89 \pm 0.01) \mathrm{cm}$. The thickness of the wall of the cylinder is

Two resistors $R_1 (24\pm 0.5) \mathrm{\Omega }$ and $R_2 (8\pm 0.3) \mathrm{\Omega }$ are joined in series. The equivalent resistance is

In a meter bridge circuit, the known resistance used in resistance box is $100 \mathrm{\Omega }$ (without any error and the unknown resistor is put in right arm). The null point is found to be $40 \mathrm{cm}$ from the left end. If $\mathrm{mm}$ scale is used in the meter bridge then the resistance of the unknown resistor is:

In the formula $X=3Y{Z}^2$, the quantities $X$ and $Z$ have the dimensions of capacitance and magnetic induction, respectively. The dimensions of $Y$ in the MKS system are,